Math word problem with prime numbers as ages?

Question

My grandson, my son [his father] and i share the same birthday . Tis year i remarked to my son " you know of course that today all three of our ages have become prime numbers. But did you realize that for the last17 years prior to this year whenever your age was a prime number so was mine and vise versa?" . yes he replied and 17 yers from now i will say to MY son " you know for the last 18 years prior to this year whenever your age was a prime number so was mine and vise versa". how old are we?

not a slightest clue as to how to do this problem

Answer 1

answer=13, 37 and 67

17 years before = father 20 and gramps 50.
a year before that, being 19 and 49, was the last time anyone of them had a prime alone.

17 years to come = son 30 and father 54.
a year before that, being 29 and 53, would be the last time they celebrate primes together. since a year after that, at 31 and 55, only son will celebrate prime.

Answer 2

Hmmm... me neither, but let's start by listing the prime numbers less than 100:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

Let's list the gaps between them too:

1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8

So we want to look for two 17 year stretches which have the same gaps between prime numbers...

Answer 3

23, 41, 59

Answer 4

present ages --------------- 23, 41 and 61

18 years back-------------- 5 , 23 and 43

after 18 years -------------- 41, 59 and 79